The GATE Grind

GATE 2025 EE – Question 50

Electromagnetic Fields · Effect of dielectric medium, Capacitance of simple configurations · 2 marks · Multiple choice

An air filled cylindrical capacitor (capacitance $C_0$) of length $L$, with $a$ and $b$ as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its cross-sectional view is shown in Fig. (i). In order to increase the capacitance, a dielectric material of relative permittivity $\epsilon_r$ is inserted inside 50% of the annular region as shown in Fig. (ii). The value of $\epsilon_r$ for which the capacitance of the capacitor in Fig. (ii), becomes $5C_0$ is

Diagram for GATE 2025 EE question 50
  1. 4
  2. 5
  3. 9
  4. 10

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) 9

Explanation

The dielectric fills half of the angle, so the filled and empty halves are two capacitors in parallel, each with half the plate area: $C=\dfrac{C_0}2+\dfrac{\epsilon_rC_0}2=\dfrac{(1+\epsilon_r)C_0}{2}$. Setting this to $5C_0$ gives $1+\epsilon_r=10$, so $\epsilon_r=9$.